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Simplifying x2 + -2.414x = 1.8 Reorder the terms: -2.414x + x2 = 1.8 Solving -2.414x + x2 = 1.8 Solving for variable 'x'. Reorder the terms: -1.8 + -2.414x + x2 = 1.8 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 -1.8 + -2.414x + x2 = 0.0 Begin completing the square. Move the constant term to the right: Add '1.8' to each side of the equation. -1.8 + -2.414x + 1.8 + x2 = 0.0 + 1.8 Reorder the terms: -1.8 + 1.8 + -2.414x + x2 = 0.0 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + -2.414x + x2 = 0.0 + 1.8 -2.414x + x2 = 0.0 + 1.8 Combine like terms: 0.0 + 1.8 = 1.8 -2.414x + x2 = 1.8 The x term is -2.414x. Take half its coefficient (-1.207). Square it (1.456849) and add it to both sides. Add '1.456849' to each side of the equation. -2.414x + 1.456849 + x2 = 1.8 + 1.456849 Reorder the terms: 1.456849 + -2.414x + x2 = 1.8 + 1.456849 Combine like terms: 1.8 + 1.456849 = 3.256849 1.456849 + -2.414x + x2 = 3.256849 Factor a perfect square on the left side: (x + -1.207)(x + -1.207) = 3.256849 Calculate the square root of the right side: 1.804674209 Break this problem into two subproblems by setting (x + -1.207) equal to 1.804674209 and -1.804674209.Subproblem 1
x + -1.207 = 1.804674209 Simplifying x + -1.207 = 1.804674209 Reorder the terms: -1.207 + x = 1.804674209 Solving -1.207 + x = 1.804674209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.207' to each side of the equation. -1.207 + 1.207 + x = 1.804674209 + 1.207 Combine like terms: -1.207 + 1.207 = 0.000 0.000 + x = 1.804674209 + 1.207 x = 1.804674209 + 1.207 Combine like terms: 1.804674209 + 1.207 = 3.011674209 x = 3.011674209 Simplifying x = 3.011674209Subproblem 2
x + -1.207 = -1.804674209 Simplifying x + -1.207 = -1.804674209 Reorder the terms: -1.207 + x = -1.804674209 Solving -1.207 + x = -1.804674209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.207' to each side of the equation. -1.207 + 1.207 + x = -1.804674209 + 1.207 Combine like terms: -1.207 + 1.207 = 0.000 0.000 + x = -1.804674209 + 1.207 x = -1.804674209 + 1.207 Combine like terms: -1.804674209 + 1.207 = -0.597674209 x = -0.597674209 Simplifying x = -0.597674209Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.011674209, -0.597674209}
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